Glycerin is a humectant, meaning it attracts moisture to your skin. Glycerin is a neutral, sweet-tasting, colorless, thick liquid which freezes to a gummy paste and which has a high boiling point. Glycerin can be dissolved into water or alcohol, but not oils. On the other hand, many things will dissolve into glycerin easier than they do into water or alcohol. Glycerin is also highly "hygroscopic" which means that it absorbs water from the air.
Example: if you left a bottle of pure glycerin exposed to air in your kitchen, it would take moisture from the air and eventually, it would become 80 per glycerin and 20 percent water.
(Note: While people say this softening is the result of the glycerin attracting moisture to your skin, there is heated debate as to whether or not the glycerin has some other properties all its own which are helpful to the skin. Summed up, the current thinking is "We know glycerin softens the skin. Some people think its because it attracts moisture, but there could be other reasons.")